Equivalent Surfaces Research Articles

The Cubo-Cubic Transformation and K3 Surfaces

In this note we observe that the Cremona transformation in Oguiso’s example of Cremona isomorphic but not projectively equivalent quartic K3 surfaces in $${\mathbb {P}}^3$$ is the classical cubo-cubic transformation of $${\mathbb {P}}^3$$.

Numerical modelling of rough particle contacts subject to normal and tangential loading

Our understanding of the mechanics of contact behaviour for interacting particles has been developed mostly assuming that surfaces are smooth. However, real particles of interest in engineering science are generally rough. While recent studies have considered the influence of roughness on the normal force–displacement relationship, surface roughness was quantified using only a single scalar measure, disregarding the topology of the surface. There are some conflicting arguments concerning the effect of roughness on the tangential or shear force–displacement relationship. In this study, optical interferometry data are used to generate the surface topology for input into a 3D finite element model. This model is used to investigate the sensitivity of the normal force–displacement response to the surface topology by considering different surfaces with similar overall roughness values. The effect of surface roughness on the tangential force–displacement relationship and the influence of loading history are also explored. The results indicate that quantifying roughness using a single value, such as the root mean square height of roughness, Sq, is insufficient to predict the effect of roughness upon stiffness. It is also shown that in the absence of interlocking, rough particle surfaces exhibit a lower frictional resistance in comparison with equivalent smooth surfaces.

Comparison of 8/6 radial and axial flux switched reluctance machines

PurposeThis paper aims to deal with a performance comparison of an 8/6 radial-flux switched reluctance machine (RFSRM) and an axial-flux switched reluctance machine (AFSRM), presenting equivalent active surfaces.Design/methodology/approachAn axial machine was designed based on the equivalent active surfaces of a radial one. After estimating the machine inductances with a reluctance network, finite elements numerical models have been implemented for a more precise inductance determination and to estimate the electromagnetic torque for both machines. Finally, the AFSRM was thoroughly examined by analyzing the impact of some geometric parameters on its performance.FindingsThe comparison of the RFSRM and AFSRM at equivalent active surfaces showed that the obtained axial machine is more compact along with an improvement in the electromagnetic torque.Practical implicationsThe equivalent AFSRM is more compact, therefore more interesting for transport and on-board applications.Originality/valueThe RFSRM and AFSRM performance comparison using the same active surfaces has not been done. Moreover, the AFSRM presented has a rare design with no rotor yoke and where the rotor teeth are encapsulated in a nonmagnetic structure, allowing a more compact design.

Flexible Serialized Complementary Coils for the Detection of Moving LF RFID Tags

This paper focuses on bats detection, tagged at low frequency (134.2 kHz) with glasstags (typically: length 15 mm and radius 1 mm). The physical link is magnetic coupling. We propose the design of a reader antenna based on a multi-coil structure. The goal is to obtain the highest surface of detection, at a distance of 10-15 cm, i.e., defining a so called “volume of detection.” The cylindrical volume of the glasstags involves a high sensitivity to the magnetic field orientation. As the bats are flying, the tags equivalent surfaces are considered with a random orientation. Using complementary coils principle enables to detect fruitfully the glasstags in two perpendicular orientations named horizontal mode (HM) and vertical mode (VM). We propose the design of a flexible reader antenna structure by means of an adhesive copper tape fixed on a cloth. The prototype is designed after CST simulations and empirical formula evaluations. Measurements show a good agreement with the modeling and tests of detection are performed with the proposed reader antenna. By comparison with a commercial antenna, the prototype reaches the highest volume of detection in both HM and VM modes and fulfills the targeted distance of detection.

An integrated approach to the Surat Basin stratigraphy

The stratigraphy of the Surat Basin, Queensland, has historically been sub-divided by formation and unit nomenclature with a few attempts by other authors to apply sequence stratigraphy to existing formation boundaries. At a local- to field-scale, lithostratigraphy may be able to represent stratigraphy well, but at regional-scale, lithostratigraphic units are likely to be diachronous. To date, this lithology-driven framework does not accurately reflect time relationships in the sub-surface. An entirely new integrated methodological approach, involving well tied seismic data and sequence stratigraphic well-to-well correlations compared with published zircon age dates, has been applied to hundreds of deep wells and shallower coal seam gas wells. This method sub-divides the Surat Basin stratigraphy into defendable 2nd order to 3rd order sequence stratigraphic cycles and has required the use of an alpha-numeric sequence stratigraphic nomenclature to adequately and systematically label potential time equivalent surfaces basin-wide. Correlation of wells is the first step in building models of aquifers and coal seam gas fields for numerical simulation of fluid flow, which is necessary for responsible resource management. Lithostratigraphic correlations will overestimate the extent and hydraulic connectedness of the strata of interest. The result may be fluid flow models that do not represent a realistic pressure footprint of the flow. The present sequence stratigraphic method more accurately reflects the disconnectedness of sub-surface coals and sandstones (aquifers) on a field-to-field scale, adjacent field-scale, and basin-wide scale. It forms the basis for improved and more representative modelling of the sub-surface.

Friction‐Stability‐Permeability Evolution of a Fracture in Granite

AbstractThe evolution of frictional strength, stability, and fracture permeability is intimately linked both to the seismic cycle and to the impact of hydraulic stimulation for fractured reservoirs. However, despite this importance, the poromechanical relationships between fault permeability and strength remain unclear. The present study explores this relationship via laboratory experiments for concurrent shear‐flow on smooth fractures of Westerly granite. The novelty of these experiments is that the shear velocity is precisely controlled during the measurement of fracture permeability. Results indicate permeability enhancement during velocity‐weakening (potentially unstable) frictional slip. To decipher key processes contributing to this response, we evaluate the state of contacting asperities and of fracture surface asperities via digital rock fracture modeling of statistically equivalent surfaces. We propose two plausible mechanisms constraining the relationship between friction and permeability evolution—one based on changes in asperity contact distribution and one on shear‐induced dilation triggered by changes in fault slip velocity. These mechanisms should be taken into account in interpreting field observation such as the abrupt permeability increase of natural faults at the onset of seismic slip.

The mid-Cretaceous Debarsu Formation (Upper Albian–Middle Turonian) of Central Iran: depositional environment, palaeogeography, and sequence stratigraphic significance

The Upper Albian–Turonian Debarsu Formation in its type area around Haftoman, south of Khur (Central Iran) has been investigated using an integrated approach of high-resolution logging, bio- and sequence stratigraphic dating, and facies analysis based on field observations and detailed microfacies studies. The up to 500-m-thick Debarsu Formation consists of stacked, several 10- to ~ 100-m-thick, essentially asymmetric shallowing-upward cycles from grey offshore marl via skeletal and intraclastic limestone with large-scale clinoformed foresets to thick-bedded bioclastic, locally rudist-bearing shallow-marine topset strata capped by palaeokarst surfaces. The diverse (micro)facies inventory (29 facies types) is dominated by skeletal carbonates (bioclastic pack-, grain-, float- and rudstone) that reflect deposition on a carbonate ramp with a lagoonal shoreline that was attached to an elevated area in the west and southwest. The outer ramp facies association of the Debarsu ramp contains predominantly microbioclastic marl with open-marine microfossils (planktic foraminifera) and fine-grained bioturbated packstone. The transition into the mid-ramp facies association, dominated by bioclastic pack- and grainstone (foreset strata), is commonly gradational. The inner-ramp facies association is very diverse, mainly consisting of high-energy (well-washed and cross-bedded) grainstone as well as back-ramp or inter-shoal bioclastic float- and rudist bafflestone. The Debarsu Formation occurs in an area of more than 2500 km2 to the west, southwest, and south of Khur but had its depocenter with maximum thicknesses and thick offshore marl intervals in the type area. The large-scale shallowing-upward cycles correspond to third-order depositional sequences. The chronostratigraphic positions of the sequence-bounding unconformities in the Upper Albian to Lower Cenomanian match equivalent surfaces known from other Cretaceous basins on different tectonic plates. However, a large-scale intraformational stratigraphic gap (Middle Cenomanian to lowermost Turonian) at a major palaeokarstic surface in the upper part of the formation must be related to tectonic uplift. The Debarsu Formation shows similarities in (sequence) stratigraphic stacking patterns to hydrocarbon-bearing formations of the southern Tethyan margin (Arabian Plate).

Edge diffraction in an anomalously reflecting half-plane

A half-plane, formed of anomalously reflecting metasurface, is taken into account. The layer is modeled by an impedance half-screen. In order to obtain the diffracted fields, the geometrical optics waves are evaluated as a sum of equivalent soft, hard and impedance surfaces. The diffracted waves are derived by the superposition of the diffracted fields from the equivalent surfaces. The uniform field expressions are obtained by the method of uniform theory of diffraction. The behaviors of the fields are studied numerically.

Volume-Enhanced Compatible Remeshing of 3D Models.

Compatible remeshing provides meshes with common connectivity structures. The existing compatible remeshing methods usually suffer from high computational cost or poor quality. In this paper, we present a fast method for computing compatible meshes with high quality. Given two closed, oriented, and topologically equivalent surfaces and a sparse set of corresponding landmarks, we first compute a bijective inter-surface mapping, from which compatible meshes are generated. We then improve the remeshing quality by using a volume-enhanced optimization. In contrast to previous work, our method designs a fast volume-enhanced improvement procedure that directly reduces the isometric distortion of the map between the compatible meshes. Our method also tries to preserve the shapes of the input meshes by projecting the vertices of the compatible meshes onto the input surfaces. Central to this approach is the use of the monotone preconditioned conjugate gradient method, which minimizes the energies effectively and efficiently. Compared with state-of-the-art methods, our method performs about one order of magnitude faster with better remeshing quality. We demonstrate the efficiency and efficacy of our method using various model pairs.

Relative sea-level changes and sedimentary facies development of the lowermost Cretaceous (Berriasian–Valanginian) cycles in the north of Ar Riyad city, Saudi Arabia

A new high-resolution stratigraphic framework for the thick and well-exposed Lower Cretaceous rocks of Saudi Arabia has been provided. The studied successions consist mainly of carbonates with minor interbedded siliciclastics, forming the Silayy, Yamamah and Buwaib formations in the study area (north of Ar Riyad city). Based on the integrated sedimentary facies analysis, a relative sea-level curve for the Berriasian–Valanginian interval has been established, including stacking pattern of the different facies cycles. Two transgressive–regressive facies cycles have been identified and documented in the studied sections. The first cycle started during the middle Berriasian (∼143 Ma), comprising the Silayy and Yamamah formations. It terminated at the Yamamah–Buwaib formational contact during the early Valanginian (∼138 Ma), characterized by a friable brownish ferruginous sandstone bed at the base of the Buwaib Formation. The second transgressive–regressive cycle encompasses the entire lower Valanginian Buwaib Formation. A major unconformity surface formed during the early late Valanginian (∼136 Ma), marking the end of the second cycle and characterized by a distinctive hardground condensation. The correlation and dating of the recognized cycles, identified in central Saudi Arabia, shows a contemporaneity to equivalent surfaces globally and thus strongly supports an isochronous formation of Berriasian–Valanginian facies cycles by eustatic sea-level changes.

Determination of Equivalent Coupling Surface of Passive Components Using the TEM Cell

The design of cheaper and more compact electromagnetic compatibility (EMC) filters can be achieved by exploiting the magnetic coupling between components. This requires the knowledge of coupling coefficients between components and, consequently, of their equivalent coupling surface. The aim of this paper is to present how this coupling surface can be determined using a transverse electromagnetic mode cell. This methodology is described and applied to two different cases: a capacitor and an inductor. In order to validate the determination and usage of equivalent coupling surfaces, a comparison between the calculation and measurement of mutual inductances is carried out on practical examples.

Quantum confinement and heavy surface states of Dirac fermions in bismuth (111) films: An analytical approach

Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is a topologically nontrivial semimetal. We derive an analytic theory of surface and size-quantized states of Dirac fermions in Bi(111) films taking into account the new data. The theory relies on a new phenomenological momentum-dependent boundary condition for the effective Dirac equation. The boundary condition is described by two real parameters that are expressed by a linear combination of the Dresselhaus and Rashba interface spin-orbit interaction parameters. In semi-infinite Bi(111), near the $\overline{\mathrm{M}}$ point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in the $\overline{\mathrm{\ensuremath{\Gamma}}}\text{\ensuremath{-}}\overline{\mathrm{M}}$ direction order of ten free electron masses and light effective mass in the $\overline{\mathrm{M}}\text{\ensuremath{-}}\overline{\mathrm{K}}$ direction order of one hundredth of free electron mass. In Bi(111) films with equivalent surfaces, the surface states from top and bottom surfaces are not split. In such a symmetric film with arbitrary thickness, the bottom of the lowest quantum confinement subband in the conduction band coincides with the bottom of the bulk conduction band in the $\overline{\mathrm{M}}$ point.

On absolute linear Harbourne constants

In the present note we study absolute linear Harbourne constants. These are invariants which were introduced in [2] in order to relate the lower bounds on the self-intersection of negative curves on birationally equivalent surfaces to the complexity of the birational map between them. We provide various lower and upper bounds on Harbourne constants and give their values for the number of lines s of the form p2r+pr+1 for any prime number p and also for all values of s up to 31. This extends considerably results of the third author obtained earlier in [10].

Some remarks on L-equivalence of algebraic varieties

In this short note we study the questions of (non-)L-equivalence of algebraic varieties, in particular, for abelian varieties and K3 surfaces. We disprove the original version of a conjecture of Huybrechts (Int J Math 16(1):13–36, 2005, Conjecture 0.3) stating that isogenous K3 surfaces are L-equivalent. Moreover, we give examples of derived equivalent twisted K3 surfaces, such that the underlying K3 surfaces are not L-equivalent. We also give examples showing that D-equivalent abelian varieties can be non-L-equivalent (the same examples were obtained independently in Ito et al. Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties. arXiv:1612.08497 ). This disproves the original version of a conjecture of Kuznetsov and Shinder (Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics. Sel Math New Ser. arXiv:1612.07193 , Conjecture 1.6). We deduce the statements on (non-)L-equivalence from the very general results on the Grothendieck group of an additive category, whose morphisms are finitely generated abelian groups. In particular, we show that in such a category each stable isomorphism class of objects contains only finitely many isomorphism classes. We also show that a stable isomorphism between two objects X and Y with $${\text {End}}(X)=\mathbb {Z}$$ implies that X and Y are isomorphic.

On solving continuum-mechanics problems by fast multipole methods

It is shown analytically and numerically that the kernel-independent fast multipole method provides the accuracy and computational complexity of the analytical method if circular (spherical in 3D) equivalent surfaces are used.

Room temperature thermally evaporated thin Au film on Si suitable for application of thiol self-assembled monolayers in micro/nano-electro-mechanical-systems sensors

Gold is a standard surface for attachment of thiol-based self-assembled monolayers (SAMs). To achieve uniform defect free SAM coatings, which are essential for bio/chemical sensing applications, the gold surface must have low roughness and be highly orientated. These requirements are normally achieved by either heating during Au deposition or postdeposition Au surface annealing. This paper shows that room temperature deposited gold can afford equivalent gold surfaces, if the gold deposition parameters are carefully controlled. This observation is an important result as heating (or annealing) of the deposited gold can have a detrimental effect on the mechanical properties of the silicon on which the gold is deposited used in microsensors. This paper presents the investigation of the morphology and crystalline structure of Au film prepared by thermal evaporation at room temperature on silicon. The effect of gold deposition rate is studied, and it is shown that by increasing the deposition rate from 0.02 to 0.14 nm s−1 the gold surface root-mean-square roughness decreases, whereas the grain size of the deposited gold is seen to follow a step function decreasing suddenly between 0.06 and 0.10 nm s−1. The x-ray diffraction intensity of the preferentially [111] orientated gold crystallites is also seen to increase as the deposition rate increases up to a deposition rate of 0.14 nm s−1. The formation and characterization of 1-dodecanethiol on these Au coated samples is also studied using the contact angle. It is shown that by increasing the Au deposition rate, the contact angle hysteresis (CAH) decreases until it plateaus, for a deposition rate greater than 0.14 nm s−1, where the CAH is smaller than 9° which is an indication of homogeneous SAM formation, on a smooth surface.

Impact of the patterned membrane morphology on PEMFC performances of ultra-low platinum loaded MEAs

Two types of patterns were achieved on the surface of NR211 membranes: holes and knolls. These patterns were produced on only one side of the membrane at the cathode. For equivalent specific surfaces, these two membrane patterning morphologies were tested in fuel cell conditions with very low platinum loading (30 μg/cm2). Catalyst loading was achieved by magnetron plasma deposition either on the microporous carbon electrode or directly on the patterned membrane. The fuel cell performances in dry conditions were found to be highly dependent on the morphology of the membrane surface. Results showed that the knoll morphology gave better fuel cell performances than the hole morphology. For the knoll morphology the current density increased by a factor of 1.78 at 0.7 V versus a pristine membrane, whereas the hole morphology appeared in some cases to deteriorate the fuel cell performances, despite an increase in the specific surface by a factor of 1.87 versus a pristine membrane. The concepts of top level (extreme surface of the patterned membranes) and bottom level (the pattern base) were introduced to highlight the phenomena of micro water management on the areas of the micro-patterns which act on the local conductivity of the protonic membranes. These results suggest that it is necessary to choose the morphology of the patterns very carefully before simply increasing the specific surface of protonic membranes.

Reflection/transmission calculation of complex particle slabs for normal incidence through dipole approximation

The computation of the reflection/transmission coefficients from normally illuminated bianisotropic metamaterial slabs through a rigorous method is presented in this paper. The bianisotropic particles that compose finite slabs are approximated as electric and magnetic dipoles. Modeling these slabs as a succession of 2D arrays, the interaction of all dipoles is described via Green’s function series, for a given wave illumination on each array, and the excited dipole moments are obtained by the resulting linear system. Finally, the reflection/transmission coefficients are derived in terms of summing the scattering from the equivalent surfaces that comprise the slab. The new algorithm is applied to a bianisotropic and a complicated chiral particle, while all results are compared to numerically simulated ones.

Water droplet impact on elastic superhydrophobic surfaces.

Water droplet impact on surfaces is a ubiquitous phenomenon in nature and industry, where the time of contact between droplet and surface influences the transfer of mass, momentum and energy. To manipulate and reduce the contact time of impacting droplets, previous publications report tailoring of surface microstructures that influence the droplet - surface interface. Here we show that surface elasticity also affects droplet impact, where a droplet impacting an elastic superhydrophobic surface can lead to a two-fold reduction in contact time compared to equivalent rigid surfaces. Using high speed imaging, we investigated the impact dynamics on elastic nanostructured superhydrophobic substrates having membrane and cantilever designs with stiffness 0.5–7630 N/m. Upon impact, the droplet excites the substrate to oscillate, while during liquid retraction, the substrate imparts vertical momentum back to the droplet with a springboard effect, causing early droplet lift-off with reduced contact time. Through detailed experimental and theoretical analysis, we show that this novel springboarding phenomenon is achieved for a specific range of Weber numbers (We >40) and droplet Froude numbers during spreading (Fr >1). The observation of the substrate elasticity-mediated droplet springboard effect provides new insight into droplet impact physics.

All molecular surfaces are equal: demanding invariance of predictions in linear single-variable models

ABSTRACTThe molecular surface has been suggested to be a region of the molecule, where information of non-covalent intermolecular interactions is present. Many workers have pursued this idea by constructing models based on statistical parameters Φ extracted from the electrostatic potential on a particular molecular surface. We claim that a better approach is to define a family of equivalent molecular surfaces, each associated with a particular electron density ε. The demand that any model must give the same predictions on all such molecular surfaces yields a mathematical requirement restricting the space of permissible parameters. We prove that linear single-variable models of the form property = α Φ + β will only yield invariant predictions if the parameter values of Φ computed on equivalent surfaces are linearly related. This claim is not restricted to the use of the electrostatic potential, but holds for any parameter extracted from the surface of molecules. By using a set of 44 molecules, we also demonstrate that a frequently used aspect of the electrostatic potential, that of ‘imbalance’ of negative and positive values, fails to satisfy the linearity requirement. It is argued that multi-variable models should only include parameters that satisfy the single-variable requirement.