Lower-dimensional Elements Research Articles

Mechanism of remote epitaxy of stanene on Cu(111) substrate through monolayer graphene linking

Graphene-coated substrates have a significant effect on regulating the commensurate epilayer growth of ionic thin-films, which has demonstrated that the polarity of atomic binding in ionic-bonded materials is strong enough to penetrate through a few-layer graphene, but that from the covalent-bonded material is screened even by a monolayer graphene (MLG). However, recent studies have demonstrated that the covalent-bonded stanene film can also be obtained by the remote heteroepitaxy on the monolayer graphene-covered Cu(111) substrate. In this work, we use first-principles calculations to uncover the microscopic mechanism of the unusual remote interactions, which facilitate the Sn adatom growth on the MLG-covered Cu substrate. Our calculations suggest that the lattice sites of MLG determine the adatom registry and provide an essential mediator role in the extended adatom-linking-substrate interactions, whereas the Cu substrate under the MLG reinforces the adsorption on the entire surface by the extended hybridization of MLG/Cu(111) interfacial states with the Sn adatom localized states. This finding provides a novel insight into the remote epitaxial mechanism of 2D films on the MLG-covered metal substrates, which opens the opportunity in the field of vdW (van der Waals) epitaxial of low-dimensional element crystalline and their transferable integration.

A Systematic Approach to Constructing Preconditioners for the $hp$-Version Mass Matrix on Unstructured and Hybrid Finite Element Meshes

We develop a systematic approach to building uniform preconditioners for the mass matrix on unstructured meshes composed of higher dimensional elements using only preconditioners for lower dimensional simplices. In particular, we show that the resulting preconditioners are automatically uniform with respect to both the mesh size h and polynomial degree $p$, and that the preconditioners can be implemented efficiently by exploiting the structure of the preconditioners on the lower dimensional elements. We illustrate the approach by developing preconditioners for prismatic elements and for the challenging case of hybrid meshes of hexahedra, prisms, and tetrahedra.

Study on the influence of randomly distributed fracture aperture in a fracture network on heat production from an enhanced geothermal system (EGS)

In the attempt to reduce the CO2 emissions to the atmosphere and therefore the dependence on fossil fuels, geothermal energy has started to receive increased scientific interest. With the development of the Enhanced Geothermal System (EGS) technology, extensive geothermal energy applications have become feasible. However, enhanced geothermal reservoirs are usually situated several kilometers below the ground, which makes their experimental investigation challenging. Therefore, numerical models capable of simulating thermohydraulic (TH) effects are an essential additional tool for analyzing geothermal reservoir efficiency. To simulate fluid migration and heat propagation within a fractured geothermal reservoir in EGS, discrete fracture models (DFMs) of the TH processes are widely used. However, the variability of aperture size from one fracture to another is typically ignored in these models. In this work, a discrete fracture model considering variable aperture fractures is presented and used to investigate the performance of a geothermal reservoir in EGS. The outlet temperature and energy production rate are used as the evaluation criteria. Statistically generated fracture networks with different apertures were applied. The fractures are represented as lower-dimensional elements. The fracture apertures are randomly distributed within the networks, but constant for one single fracture. The simulation results show that the coefficient of variation of the DFN apertures strongly affects the performance of the geothermal reservoir. The heat production rate and outlet temperature can be divided into three stages based on the value of coefficient of variation of fracture apertures. The higher variability results in the low heat production rate but high outlet temperature. The investigation on fracture density in turn indicates that the average heat production rate is proportional to the fracture density. However, the effect of fracture density is reduced with an increase of coefficient of variation. Furthermore, the comparison between fracture aperture and fracture density shows that, the increase in mean fracture aperture leads to a higher increase in average heat production rate than an increase in fracture density.

Muscle Synergies in Parkinson's Disease.

Over the last two decades, experimental studies in humans and other vertebrates have increasingly used muscle synergy analysis as a computational tool to examine the physiological basis of motor control. The theoretical background of muscle synergies is based on the potential ability of the motor system to coordinate muscles groups as a single unit, thus reducing high-dimensional data to low-dimensional elements. Muscle synergy analysis may represent a new framework to examine the pathophysiological basis of specific motor symptoms in Parkinson’s disease (PD), including balance and gait disorders that are often unresponsive to treatment. The precise mechanisms contributing to these motor symptoms in PD remain largely unknown. A better understanding of the pathophysiology of balance and gait disorders in PD is necessary to develop new therapeutic strategies. This narrative review discusses muscle synergies in the evaluation of motor symptoms in PD. We first discuss the theoretical background and computational methods for muscle synergy extraction from physiological data. We then critically examine studies assessing muscle synergies in PD during different motor tasks including balance, gait and upper limb movements. Finally, we speculate about the prospects and challenges of muscle synergy analysis in order to promote future research protocols in PD.

Simulation of 3D flow and solute transport in fractured rock at Äspö, Sweden

The code d3f++ developed under the leadership of GRS for simulating 3D flow and solute transport includes an advanced formulation for fracture flow and transport in lower-dimensional elements that has still been in need of qualification. A variety of in-situ experiments in the granitic rock at the Swedish Hard Rock Laboratory Aspo offers an excellent basis for this purpose. Particularly well suited is the work performed in the TRUE Block Scale Project where a hydrostructural model comprising 30 large-scale fractures in a cube-shaped domain with a side length of 200 m has been set up for simulating groundwater flow which in turn forms the basis for reproducing the results of the injection–extraction tracer test “C2”. The present paper deals with modelling 3D flow and solute transport with the code d3f++ as a qualification exercise. The modelling results reveal an excellent representation of the contrasts in flow velocity across the fractures. Also the jumps in tracer concentration along intersecting fractures where waters with different tracer concentrations mix are handled well by the code. Calibration has nevertheless been required in order to achieve a reasonable fit of measured and calculated breakthrough curves.

The Polytope of Hereditary Information the Structure, Location, Signification

The geometry of the neighborhood of the compound of two nucleic acid helices with nitrogen bases was investigated. It is proved that this neighborhood is a cross-polytope of dimension 13 (polytope of hereditary information), in the coordinate planes of which there are complementary hydrogen bonds of nitrogenous bases. The structure of this polytope is defined, its image is given. The total incident flows from the low-dimensional elements to the higher-dimensional elements and vice versa of the hereditary information polytope are calculated equal to each other. High values of these flows indicate a high intensity of information exchange in the polytope of hereditary information that ensures the transfer of this information

The Structure of the Polytope of Hereditary Information

The representations of the sugar molecule and the residue of phosphoric acid in the form of polytopes of higher dimension are used. Based on these ideas and their simplified three-dimensional images, a three-dimensional image of nucleic acids is constructed. The geometry of the neighborhood of the compound of two nucleic acid helices with nitrogen bases has been investigated in detail. It is proved that this neighborhood is a cross-polytope of dimension 13 (polytope of hereditary information), in the coordinate planes of which there are complementary hydrogen bonds of nitrogenous bases. The structure of this polytope is defined, and its image is given. The total incident flows from the low-dimensional elements to the higher-dimensional elements and vice versa of the hereditary information polytope are calculated equal to each other. High values of these flows indicate a high intensity of information exchange in the polytope of hereditary information that ensures the transfer of this information.

Spatial ANCF/CRBF beam elements

In this paper, the consistent rotation-based formulation (CRBF) is used to develop new three-dimensional beam elements starting with the absolute nodal coordinate formulation (ANCF) kinematic description. While the proposed elements employ orientation parameters as nodal coordinates, independent rotation interpolation is avoided, leading to unique displacement and rotation fields. Furthermore, the proposed spatial ANCF/CRBF-based beam elements adhere to the noncommutative nature of the rotation parameters, allow for arbitrarily large three-dimensional rotation, and eliminate the need for using co-rotational or incremental solution procedures. Because the proposed elements have a general geometric description consistent with computational geometry methods, accurate definitions of the shear and bending deformations can be developed and evaluated, and curved structures and complex geometries can be systematically modeled. Three new spatial ANCF/CRBF beam elements, which use absolute positions and rotation parameters as nodal coordinates, are proposed. The time derivatives of the ANCF transverse position vector gradients at the nodes are expressed in terms of the time derivatives of rotation parameters using a nonlinear velocity transformation matrix. The velocity transformation leads to lower-dimensional elements that ensure the continuity of stresses and rotations at the element nodal points. The numerical results obtained from the proposed ANCF/CRBF elements are compared with the more general ANCF beam elements and with elements implemented in a commercial FE software.

Modelling of multi-lateral well geometries for geothermal applications

Abstract. Well inflow modelling in different numerical simulation approaches are compared for a multi-lateral well. Specifically radial wells will be investigated, which can be created using Radial Jet Drilling (RJD). In this technique, powerful hydraulic jets are used to create small diameter laterals (25–50 mm) of limited length (up to 100 m) from a well. The laterals, also called radials, leave the backbone at a 90∘ angle. In this study we compare three numerical simulators and a semi-analytical tool for calculating inflow of a radial well. The numerical simulators are FE approaches (CSMP and GOLEM) and an FV approach with explicit well model (Eclipse®). A series of increasingly complex well configurations is simulated, including one with inflow from a fault. Although all simulators generally are reasonably close in terms of the total well flow (deviations < 4 % for the homogeneous cases), the distribution of the flow over the different parts of the well can vary significantly. Also, the FE approaches are more sensitive to grid size when the flow is dominated by radial flow to the well since they do not include a dedicated well model. In the FE approaches, lower dimensional elements (1-D for the well and 2-D for the faults) were superimposed into a 3-D space. In case the flow is dominated by fracture flow, the results from the FV approach in Eclipse deviates from the FE methods.

Modelling coupled fluid flow and heat transfer in fractured reservoirs: description of a 3D benchmark numerical case

One challenge of modelling coupled fluid flow and heat transfer within geological reservoirs lies in representing the geometry of fractures and to formulate the physics of their hydraulic behaviours. This contribution presents a 3D case to be used to test the ability of simulators in solving for such issues. The reliability of the study is tested against three simulators (GOLEM, OpenGeosys, and Feflow), which integrates fractures as single-nodded lower dimensional elements embedded in the rock matrix. Comparing the results we can conclude on the validity of the synthetic model as a code benchmarking case for simulators adopting a similar approach.

Finite-difference time-domain analysis of the vibration characteristics of building structures using a dimension-reduced model

In order to accurately predict the vibration characteristics of buildings, wave-based numerical methods are effective from the viewpoint of the modeling accuracy of the physical mechanism and the detailed geometries of the simulated field. However, because of the performance of current PCs, the prediction of real-scale problems remains difficult. In order to address such problems, we herein propose a vibration simulation method for a beam-plate structure using a dimension-reduced modeling method. The target structure is modeled as a composite structure consisting of two-dimensional plate elements and one-dimensional beam elements, which are coupled based on the implicit finite-difference approximation scheme. By applying such a low-dimensional element, a faster simulation that requires less memory, as compared with a three-dimensional discretization scheme, is made available. To validate the method, the vibration characteristics obtained by the proposed scheme are compared to the measured results for model-scale and full-scale structure. The comparison of the measurement and simulation results suggest that the proposed method can be used to accurately simulate a multilayered building structure.

Finite-difference time-domain analysis of the vibration characteristics of a beam-plate structure using a dimension-reduced model

In order to accurately predict the vibration characteristics of structure-borne sound transmission in buildings, wave-based numerical methods are effective from the viewpoint of the modeling accuracy of the physical mechanism and the detailed geometries of the simulated field. However, because of the performance of current PCs, the prediction of real-scale problems remains difficult. In order to address such problems, we herein propose a vibration simulation method for a beam-plate structure using a dimension-reduced modeling method. The target structure is modeled as a composite structure consisting of two-dimensional plate elements and one-dimensional beam elements, which are coupled based on the implicit finite-difference approximation scheme. By applying such a low-dimensional element, a faster simulation that requires less memory, as compared with a three-dimensional discretization scheme, is made available. Good agreement between the measured and simulated results for the vibration characteristics of acrylic beam-plate models indicates the validity of the proposed method.

The secondary differentials on the third line of the Adams spectral sequence

Let p ⩾ 5 be an odd prime. In this paper the third line Ext A ∗ 3 , ∗ ( Z / p , Z / p ) of the Adams spectral sequence (ASS) is divided into the direct sum of three sub-modules, say T, C and N. We proved that the generators of T are in the images of the Thom map, and the generators of C can survive to some low dimensional elements of the Adams–Novikov spectral sequence (ANSS). Thus they have trivial secondary Adams differentials. By computing the Adams differentials induced by d 2 ( h i + 1 ) = a 0 b i and the matrix Massey products, we determined the secondary Adams differentials on the generators of N.

A mixed-dimensional finite volume method for two-phase flow in fractured porous media

We present a vertex-centered finite volume method for the fully coupled, fully implicit discretization of two-phase flow in fractured porous media. Fractures are discretely modeled as lower dimensional elements. The method works on unstructured, locally refined grids and on parallel computers with distributed memory. An implicit time discretization is employed and the nonlinear systems of equations are solved with a parallel Newton-multigrid method. Results from two-dimensional and three-dimensional simulations are presented.

Line element fields on manifolds

element fields, then the characteristic classes can be expressed in terms of lower dimensional elements. In particular, if k = n, the Stiefel-Whitney classes are expressible as elementary symmetric functions of one dimensional classes and the Pontrjagin classes as elementary symmetric functions of the Bocksteins of these one dimensional classes. In ?3, we give necessary and sufficient conditions that an orientable four dimensional manifold have four independent line element fields. As an application, we give an example of a fourdimensional non-parallelizable orientable manifold with four independent line element fields. 1. The main theorems. Let 0(n) denote the orthogonal group of nXn matrices, SO(n) C 0(n) the special orthogonal group, and Q(n), SQ(n) the subgroups of diagonal matrices in 0(n), SO(n) respectively. Clearly Q(n) Z and SQ(n) : Z` For each integer k, 0 < k < n, we define a subgroup G(k) C 0(n) to consist