Finite Plane Research Articles

Determination of Megathrust Rupture Processes Using Plate-Interface-Based Fault Models and 3D Green’s Functions: An Application to the 2011 Mw 9.1 Tohoku Earthquake

In order to understand physical processes of megathrust earthquakes, and thus to analyze hazards of the regions, proper information of the rupture processes is essential. In this study, we develop a technique for determination of large spatial-scale rupture processes on megathrust faults in subduction zones as soon as possible, based on teleseismic broadband full-waveform inversions using realistic models of finite fault geometries and 3D global velocity structures. Finite fault geometry models are constructed for eleven subduction zones of the circum-Pacific area, utilizing the 3D plate interface model Slab 1.0 of USGS. Green’s functions for available pairs of subfaults and globally distributed stations to be used in the inversions are computed in the global 3D velocity model using spectral element method rather than in a 1D velocity model. This scheme accommodates synthetic waves with lateral velocity variations especially for surface waves, which is useful in estimations of large spatial-scale slip distributions. The data utilized are teleseismic broadband full-waveform records including body waves and surface waves at the epicentral distance of 30o ~ 80o. The observed data are inverted for fault rupture processes, based on the non-negative least-square technique with a multiple source time window scheme for each subfault. The applicability of the method is tested for the 2011 Mw 9.0 Tohoku-Oki earthquake, and the result shows that the proposed scheme of the finite fault inversion produces reasonable results of slip distributions.

Domination number of incidence graphs of block designs

For a 2-(v, k, λ) design D, the incidence graph of D is a bipartite graph with vertex set P∪B, the point x∈P is adjacent to the block B∈B if and only if x is contained in B. In this paper, we investigate the domination number of the incidence graphs of symmetric 2-(v, k, λ) designs and Steiner systems. Moreover, we give a sufficient condition for a design to be super-neat, and thus prove that the finite projective planes and the finite affine planes are super-neat.

New strongly regular graphs from finite geometries via switching

We show that the strongly regular graph on non-isotropic points of one type of the polar spaces of type U(n,2), O(n,3), O(n,5), O+(n,3), and O−(n,3) are not determined by its parameters for n≥6. We prove this by using a variation of Godsil-McKay switching recently described by Wang, Qiu, and Hu. This also results in a new, shorter proof of a previous result of the first author which showed that the collinearity graph of a polar space is not determined by its spectrum. The same switching gives a linear algebra explanation for the construction of a large number of non-isomorphic designs.

Evaluating long-duration blast loads on steel columns using computational fluid dynamics

Long-duration blasts are typically defined by positive pressure durations exceeding 100 ms. Such blasts can generate dynamic pressures (blast winds) capable of exerting damaging drag loads on comparatively slender structural components such as columns. With limited drag coefficient availability for specific structural geometries, Computational Fluid Dynamics (CFD) can be the only satisfactory approach for analysing blast loading on user-specified, finite geometries. The ability to analyse long-duration blasts with commercially available CFD programmes is still not confidently offered, with no prior studies examining the accuracy of modelling interaction with relatively much smaller, finite geometries. This paper presents a comparative investigation between numerical and experimental results to assess the predictive capacity of inviscid Eulerian CFD as a method for calculating long-duration blast drag loading on finite cross-sectional geometries. Full-scale long-duration blast experiments successfully measured surface pressure–time histories on a steel I-section column aligned at four orientations. Calculated pressure–time histories on exposed geometry surfaces demonstrated good agreement although reduced accuracy and under-prediction occurred on shielded surfaces manifesting as overestimated net loading. This study provides new understanding and awareness of the numerical capability and limitations of using CFD to calculate long-duration blast loads on intricate geometries.

Literature Review on All-Optical Photonic Crystal Encoders and Some Novel Trends

The all-optical encoder (AOE) based on photonic crystals (Ph.Cs.) is one of the most important devices in computing systems. The essential related parameters are the delay time, the switching speed and the contrast ratio (CR). Moreover, the design simplicity, the compact size and the multi-wavelength operation have come as a fabrication and functional relevant attributes. Throughout the upcoming lines, an introduction for the important assessment factors and definitions will be presented. Finite difference time domain (FDTD) and plane wave expansion (PWE) methods were used for analyzing all structures. An intensive overview of the photonic crystals (AOE) was achieved for the recently published (4x2) and (8x3) types. The corresponding functional parameters for each design were explored, and comparison tables were organized. Finally, numerical methods were discussed with the accompanying commercial software packages; then a future view for the higher-performance operation was attained.

A Nonlocal Theory of Current-Driven Low-Frequency Modes in a Magnetized Strongly Coupled Collisional Dusty Plasma

The nonlocal theoretical model developed to observe current-driven low-frequency electrostatic modes in a collisional magnetized strongly coupled dusty plasma, in the strongly coupled kinetic regime ωτ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ≫ 1 (i.e., wave frequency is much larger than the dust particle relaxation time) led to a new set of equations for dispersion relation, frequency, and the growth rate. The theoretical investigations on a cylindrical magnetized strongly coupled dusty plasma led to a current driven ion dust hybrid like longitudinal dust wave propagating nearly along radial direction and a peculiar transverse shear dust wave mode along axial direction. Dispersion properties of both longitudinal dust acoustic modes and transverse shear modes are modified in the presence of ion and dust currents and the effective perpendicular wave number provided by finite geometry of strongly coupled magnetized dusty plasma. The magnetic field has a destabilizing effect on the growth of longitudinal wave modes, while the dependence of transverse modes on the strength of magnetic field is not prominent. Transverse shear modes are characterized as the short wavelength modes with a long wavelength cutoffs. A comparison of nonlocal effects with local effects shows that in bounded magnetized strongly coupled dusty plasmas, the longitudinal wave modes need a large magnetic field and weak collisional regime to support the excitation of dust wave modes, whereas the transverse modes are a consequence of viscous and collisional damping.

Expected Probabilistic Detection and Sink Connectivity in Wireless Sensor Networks

Given that a finite number of object-detecting sensors are independently and uniformly distributed at random in a finite rectangular plane of which a sink is located at the center, we derive two mathematical formulae. One is for the expected detection probability at any arbitrary point, and the other is for the expected degree of sink connectivity for any sensor node that cannot directly transmit to the sink. In this paper, we assume that the sensing model is Gaussian-like and a function of distance away from the sensor node, while the connectivity model is a binary disk. With consideration of border effects, the striking accuracy of our formulae was demonstrated by the result comparisons with simulations in various scenarios. Our work here can be used to predict the levels of coverage and connectivity. It can determine the values of related parameters for specific degrees of coverage and connectivity. When examining both coverage and connectivity together, our work shows that the relationship between coverage and connectivity is not straightforward. Finally, the formulae can be utilized in planning uncoordinated node scheduling schemes, analyzing the fault tolerance of networks in which the sensor nodes independently and randomly die, and optimizing the deployment cost from different sets of homogeneous SNs.

A characterization of the known finite Minkowski planes in terms of Klein–Kroll types with respect to $$\mathcal {G}$$-translations

Klein and Kroll classified Minkowski planes with respect to subgroups of Minkowski translations. In this paper we investigate finite Minkowski planes with respect to groups of automorphisms of Klein–Kroll type at least D with respect to $$\mathcal {G}$$ -translations. We show that type E is not possible as the type of a finite Minikowski plane and that type F characterizes the known finite Minkowski planes among finite Minkowski planes.

Spectral estimators for finite non-commutative geometries

A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addresses the question of how to extract information about these geometries from the spectrum of the Dirac operator. Since the Dirac operator is a finite-dimensional matrix, the usual asymptotics of the eigenvalues makes no sense and is replaced by measurements of the spectrum at a finite energy scale. The spectral dimension of the square of the Dirac operator is improved to provide a new spectral measure of the dimension of a space called the spectral variance. Similarly, the volume of a space can be computed from the spectrum once the dimension is known. Two methods of doing this are investigated: the well-known Dixmier trace and a recent improvement due to Abel Stern. Finally, the distance between two geometries is investigated by comparing the spectral zeta functions using the method of Cornelissen and Kontogeorgis. All of these techniques are tested on the explicit examples of the fuzzy spheres and fuzzy tori, which can be regarded as approximations of the usual Riemannian sphere and flat tori. Then they are applied to characterise some random fuzzy spaces using data generated by a Monte Carlo simulation.

Application of 3D-DDA integrated with unmanned aerial vehicle–laser scanner (UAV-LS) photogrammetry for stability analysis of a blocky rock mass slope

In stability analysis of discontinuity-controlled slopes, the rationality of results is related to the accuracy of three-dimensional (3D) slope morphology and the reliability of the discontinuity survey. With the advent of remote sensing technologies for engineering geological surveys and slope stability analyses, step-change increases have been made in the quality of data available and geometrical characterization of rock slopes. Although these techniques are frequently employed in the characterization of slope geometry and joint surfaces at present, limited research has been undertaken to effectively process the derived data and improve the quality in the reconstruction of slope geometry imported into 3D discontinuous numerical models. In this paper, an integrated system coupling 3D-DDA and UAV-LS photogrammetry is presented as a tool to evaluate the stability of a blocky rock mass slope. The system includes a UAV-LS module, a modeling module, a block-generation module, and a 3D-DDA calculation module. In the UAV-LS module, the use of UAV-LS system integrated with field mapping and site observations allows the acquisition of detailed outputs (point clouds) on both the slope and discontinuity geometry. An effective combination of commercial software Geomagic and Hyperworks is used in the modeling module to process oceans of 3D point cloud data and construct complex 3D geometrical models based on reverse engineering. In the block-generation module, the three-dimensional discontinuous deformation analysis (3D-DDA) method is then carried out in order to simulate the movement of potentially unstable blocks, within which an independent block-cutting algorithm is used to generate the blocks with arbitrary shapes and the finite structural planes similar to the real cases. The 3D-DDA calculation module uses 3D-DDA calculation algorithm to derive the simulation results. The capability of the proposed system for stability analysis of a jointed slope is demonstrated by a practical example.

Design for realizing an all-optical terahertz wave half adder based on photonic crystals

Terahertz wave half adders are one of the key logic devices required in terahertz wave communication systems and signal processing systems. In this paper, we aim to design an optical structure for realizing half-adder operation based on the multiple-mode interference effect. The central frequency of the logic device is 1.05 THz. By injecting terahertz wave signal into the input ports of the structure, the desired logic states are achieved and the resulting truth table verifies the functionality of the designed half adder. The simulation results based on the finite difference time domain and plane wave expansion methods show that the designed structure with the feasibility can be used in terahertz wave integrated digital circuits.

Mesozoic – Cenozoic evolution of the Southern Patagonian Andes fold and thrust belt (47°–48°S): Influence of the Rocas Verdes basin inversion and onset of Patagonian glaciations

The Southern Patagonian Andes (SPA) between 47°–48°S are characterized by relatively high elevations (1500–4000 m) and a 200-km-wide, largely exhumed, basement domain along the backbone of the Cordillera, bounded by a narrow 30-km-wide fold and thrust-belt to the east. The tectonic evolution of the SPA includes widespread Jurassic extension during the opening of the Austral-Magallanes basin and the Rocas Verdes back-arc oceanic basin (RVB), followed by Cretaceous to Cenozoic shortening. Although the main phases of deformation that affected this Andean segment have been the focus of previous studies, its finite geometry and step by step structural and kinematic evolution have not been quantitatively determined. In this work, we present kinematically restored cross sections, showing the variable geometry, trough time, of the eastern basement domain and the fold and thrust-belt. A regional westward-dipping listric decollement, interpreted as formed during the Jurassic extensional event, was reactivated during the Andean deformation constituting the main detachment surface of basement structures and the fold and thrust belt. West verging faults systems are considered a consequence of inversion of north-south trending extensional features as passive roof high-angle west-vergent faults. Using regional data such as field relations, unconformities, and existing ages to differentiate deformational stages, three main phases of contractional deformation are proposed for the area, starting with an Aptian - Cenomanian? phase related to inversion of the extensional depocenter in inmediate response to the closure of northernmost RVB. A second, Miocene phase responsible for most of the shortening occurred between 18 Ma and 10 Ma. Finally, the onset of glaciations and glacial erosion might have triggered out-of-sequence thrusting in the interior of the orogen after 7 Ma.

Finite rotation exact geometry solid‐shell element for laminated composite structures through extended SaS formulation and 3D analytical integration

SummaryA nonlinear exact geometry hybrid‐mixed four‐node solid‐shell element using the sampling surfaces (SaS) formulation is developed for the analysis of the second Piola‐Kirchhoff stress that extends the authors' finite element (Int J Numer Methods Eng. 2019;117:498‐522) to laminated composite shells. The SaS formulation is based on choosing inside the layers the arbitrary number of SaS parallel to the middle surface and located at Chebyshev polynomial nodes in order to introduce the displacements of these surfaces as basic shell unknowns. The external surfaces and interfaces are also included into a set of SaS. The proposed hybrid‐mixed solid‐shell element is based on the Hu‐Washizu variational principle and is completely free of shear and membrane locking. The tangent stiffness matrix is evaluated by efficient three‐dimensional (3D) analytical integration. As a result, the developed exact geometry solid‐shell element exhibits a superior performance in the case of coarse meshes and allows the use of load increments, which are much larger than possible with existing displacement‐based solid‐shell elements. It could be useful for the 3D stress analysis of thick and thin doubly curved laminated composite shells because the SaS formulation gives the possibility to obtain the 3D solutions with a prescribed accuracy.

Coulomb Mechanics and Relief Constraints Explain Landslide Size Distribution

AbstractDespite the idea that topography could control landslide size scaling law, the contribution of landscape geometry to landslide size distribution remains elusive. We define a simple mechanical model accounting for the complexity and variability of natural hillslopes to infer the landslide depth probability density function (PDF) in a given landscape and upscale it to landslide area PDF. This model is based on both a Mohr‐Coulomb stability analysis, accounting for cohesion and friction, and a criterion of intersection between rupture planes and the topographic surface. It can reproduce the distribution of observed landslide areas triggered by several past events. We found the ranges of effective cohesion (10–35 kPa) and friction (20–45°) consistent with previous estimates of large‐scale rock strength. Using synthetic topographies, we found that the finite geometry of hillslopes (length, steepness, and concavity) exerts a first‐order control on the PDF of landslide areas, especially for large landslides.

Magmatic ocean-continent transitions

Abstract Continental extension may, or may not, be coeval with significant mantle melting, leading to the formation of distinct types of passive margins (respectively magma-poor or volcanic), with distinct crustal structures. Especially in inter-cratonic mobile areas, magmatic breakup and development of volcanic passive margins (VPMs) may postdate the early development of a non-magmatic continental rift system. The time-span between the amagmatic and the magmatic systems may be relatively short or, conversely, long (tens of millions years). Such evolution is often associated with a significant apparent asymmetry in the wideness of conjugate VPMs. In this paper, we attempt to re-interpret the structure of three paired VPMs which developed close to, but separately from, a previous amagmatic aborted rift system. Due to opposite dips in major crustal detachment faults accommodating extension from sedimentary to volcanic stages, those composite margins tend to individualize a fault-dissected continental block (here designed as L-Block) along one of the conjugate margins. In addition to the amount and distribution of amagmatic extension, the time-span between amagmatic and magmatic extension exerts a major structural and rheological control on the final structure of the ocean-continent transitions. The finite margin geometry may be erroneously interpreted as resulting from a continuous process from hyperextension to the final magmatic breakup. However, the early syn-sedimentary extension appears, in many cases, to be low-rate or episodic. Consequently, the VPM final breakup of the lithosphere may shift away from the original amagmatic stretched area to the rifted margin.

Design of photonic crystal based optical digital to analog converters

The future of telecommunication and optical communication networks is extremely focused on the design and development of photonic integrated circuits (PICs). Photonic crystals play the foremost role in realizing all optical integrated circuits. Every single optical component required to be integrated in PICs can be outlined based on the requirement of the application and can be obtained with the photonic band gap property of photonic crystals. Numerous works on different optical components has been done using photonic crystals. Among which, optical digital-to-analog converters (DACs) need to be explored and attended to incorporate into PICs. In this paper, photonic crystal-based 1-bit and 2-bit DACs, suitable for the photonic integrated circuits application, are proposed. Photonic crystal ring resonators and waveguides were integrated into the reported structures. The Kerr effect of the ring resonators has been utilized to provide an average error of 4.8477% for a 2-bit optical DAC. The devised structure provides an insertion loss of −5.5596 dB, with an overall dimension of 358 µm2. The DAC structures were simulated using finite difference time domain and plane wave expansion methods.

On the Distribution of the First Break Down in the Wireless D2D Communication with Cashing

The numerical simulation of the distribution of the period before the first break down in the wireless D2D communication is analyzed while the transmitters and receivers are moving in stochastic manner. The random trajectories are generating with the use of non-stationary Fokker-Planck equation for coordinates difference on the finite plane. The effect of cashing on the duration of continuous connection is investigated. The generation method for non-stationary stochastic process trajectories enables to solve several problems in the area of stochastic control, connecting with self-organization effects, and for analysis of steady connection between transmitter and receiver devices in wireless network.

Investigation of resonant mode sensitivity in PhC based ring resonators

Quality factor and refractive index sensitivity are significant parameters in designing optical devices based on ring resonators such as filters, demultiplexers, switches in which the ring resonator is considered as an elementary componant. In this paper, we propose a photonic crystal ring resonator with super-ellipse shaped core. The proposed ring resonator placed between two parallels waveguides (bus waveguide and drop waveguide). The transmission efficiency of the proposed ring resonator at λ = 1547.3 nm is about 95% with bandwidth and quality factor values equal to 0.7 nm and 2210, respectively. Simulation results show that the resonance sensitivity upon refractive index variation of coupling, outer layer, adjacent and scattering rods are Δλ/Δn = 0.2 nm/0.01, Δλ/Δn = 0.225 nm/0.01, Δλ/Δn = 0.125 nm/0.01 and Δλ/Δn = 0.05 nm/0.01, respectively. The finite different time domain and plane wave expansion methods are used to calculate the outputs spectrum and band gap, respectively.

One-factorisations of complete graphs arising from hyperbolae in the Desarguesian affine plane

In a recent paper Korchmaros et al. (J Combin Theory Ser A 160:62–83, 2018) the geometry of finite planes is exploited for the construction of one-factorisations of the complete graph $$K_n$$ from configurations of points in $$\mathrm {PG}(2,q)$$ . Here we provide an alternative procedure where the vertices of $$K_n$$ correspond to the points of a hyperbola in $$\mathrm {AG}(2,q)$$ . In this way, we obtain one-factorisations for parameters which are either not covered by the constructions in Korchmaros et al. (J Combin Theory Ser A 160:62–83, 2018), or isomorphic to known examples but arising from different geometric configurations.

Optical emission spectroscopy and collisional-radiative modeling for low temperature Ar plasmas

Reliability of electron temperature and density diagnostics by an optical emission spectroscopy and a collisional radiative modeling is investigated by being compared with a Langmuir probe diagnostics for capacitively-coupled and inductively-coupled Ar plasmas in the ranges of electron temperature 1.2–2.2 eV and density 4.0×109−8.0×1011cm−3. Particular attention has been paid to radiation trapping and electron energy distribution function (EEDF) regarding the modeling. It is found that the two-temperature EEDF model gives better agreement of electron temperature diagnostics with the Langmuir probe measurement for non-Maxwellian plasma. The radiation trapping with an escape factor for finite size cylinder geometry reduces the discrepancy between the modeled and measured spectral line intensities compared to an escape factor for plane parallel geometry, specially for the optically thick 811.5 nm transition to the metastable level whose population depends on the diffusion rate.