Guaranteeing the topology of an implicit surface polygonization for interactive modeling

The advantage of functional methods for shape metamorphosis is the automatic generation of intermediate shapes possible between the key shapes of different topology types. However, functional methods have a serious problem: shape interpolation is applied without topological information and thereby the time values of topological changes are not known. Thus, it is difficult to identify the time intervals for key frames of shape metamorphosis animation that faithfully visualize the topological evolution. Moreover, information on the types of topological changes is missing. To overcome the problem, we apply topological analysis to functional linear shape metamorphosis and classify the type of topological evolution by using a Hessian matrix. Our method is based on Morse theory and analyzes how the critical points appear. We classify the detected critical points into maximum point, minimum point, and saddle point types. Using the types of critical points, we can define the topological information for shape metamorphosis. We illustrate these methods using shape metamorphosis in 2D and 3D spaces.

Topology-controllable Implicit Surface Reconstruction Based on Persistent Homology

BiTe, a member of the (Bi2)m(Bi2Te3)n homologous series, possesses natural van der Waals-like heterostructure with a Bi2 bilayer sandwiched between the two [Te-Bi-Te-Bi-Te] quintuple layers. BiTe exhibits both the quantum states of weak topological and topological crystalline insulators, making it a dual topological insulator and a suitable candidate for spintronics, quantum computing and thermoelectrics. Herein, we demonstrate that the chemical bonding in BiTe is to be metavalent, which plays a significant role in the pressure dependent change in the topology of the electronic structure Fermi surface. The enhancement of the metavalent bonding character with pressure in BiTe is evidenced from first-principles density functional theory (DFT) calculations. Due to the change in the Fermi surface topology, we have visualized electronic topological transitions (ETT) at ~1 and ~3 GPa through pressure dependent synchrotron X-ray diffraction analysis and Raman spectroscopy. The correlation between the metavalent bonding and ETT offers insights into chemical bonding influenced transitions in quantum materials.

Leaky dominant mode propagation regimes of a conductor-backed coplanar strip line are rigorously analyzed using the concept of critical or equilibrium points from catastrophe and bifurcation theories, in conjunction with a full-wave integral equation solution. The existence of nondegenerate or Morse critical points (MCPs) and degenerate or fold (turning) critical points (FPs) in coupling and leakage regions are associated with the occurrence of improper real and complex (leaky) solutions. The locations and types of critical points determine the stability and instability of the transmission line system with respect to small changes in geometrical parameters. The dispersion behavior of improper real and complex (leaky) solutions are efficiently reproduced in the local neighborhood of MCPs and FPs using a Taylor series expansion about those points. The qualitative and quantitative dynamic behavior of the transmission line modes can be investigated by examining the evolution of nondegenerate and degenerate points versus some structural parameter, such as strip width. The proposed analysis enables the prediction of bifurcation situations and the existence of improper real and complex solutions and gives a complete description of the system's structural behavior.

Surface modification by substitution: Changing topology of conformational potential energy surfaces

Many motion planning algorithms use Morse functions to characterize the free space. Specifically, these algorithms look at the critical points of a Morse function to denote the topological changes in the free space. This paper introduces methods to sense critical points and ensure all critical points are seen by a coverage algorithm. Experimental results performed on a mobile robot are also presented.

The paper explores the influence of topology changes (due to the change in transmission branch on/off status) and injection perturbations (due to economic load/generation redispatching) on the eigenvalue sensitivity of the power system dynamic model. These control actions are analyzed as part of dynamic transmission topology control. An algorithm for fast updates of the system matrices (in descriptor form) and without additional full matrix inversions for topology changes is proposed. To further reduce the computation time, only critical, right-most (poorly damped) and most sensitive poles to multiple input parameter changes are calculated by subspace accelerated Rayleigh quotient iteration (SARQI) and Sensitive Pole algorithms, respectively. The described approach is applied to two (small- and medium-scale) test power systems.

Pirfenidone is Associated with Decreased Indexed End Diastolic and Systolic Volumes in Patients with HFpEF and a Known History of Idiopathic Pulmonary Fibrosis

Morse theory describes the relationship between a function’s critical points and the homotopy type of the function’s domain. The theorems of Morse theory were developed specifically for functions on a manifold. This work adapts these theorems for use with parameterized families of implicit surfaces in computer graphics. The result is a theoretical basis for the determination of the global topology of an implicit surface, and supports the interactive modeling of implicit surfaces by direct manipulation of a topologically-correct triangulated representation.

Converting from implicit surfaces into polygons and further optimization are a preprocessing step in rendering implicit surfaces for visualization and other uses. This paper describes a simple method for accurate polygonization of implicit surfaces with sharp features. First, an initial coarse mesh is generated by traditional Marching Cubes (MC) method, Then the mesh is used to approximate the implicit surface with simultaneous control of mesh vertex positions, regularity and normals. The refined mesh finally converges to a limit mesh which represents a high quality approximation of the implicit surface. To reconstruct small surface features, the optimization process combines with a curvature dependent mesh adaptive subdivision. For analyzing how close the refined mesh approximates the implicit surface, two error metrics are applied. One measures the deviations of the mesh vertices from the implicit surface, while the other measures the deviations of the mesh normals from the implicit surface.

The topological aspect of the dynamics of electrons in a crystal (band electrons) and of crystal lattice vibrations (phonons) is discussed. The main features of the dynamics of conduction electrons in metals are connected with the shape of their Fermi surface, which is different from that for free electrons. It is demonstrated that the behavior of band electrons under the influence of external electric and magnetic fields depends strongly on the topology of the Fermi surface. Various examples of such a dependence (calculation of the periods of quantum oscillations, magnetic breakdown, features of the magnetoresistance, Bloch oscillations) are adduced and discussed. The features of the dynamics of phonons are manifested in singularities of the density of vibrational states (van Hove singularities), which are directly related to a change in the topology of the constant-frequency surfaces. The presence of a topological invariant that changes by a jump upon a change in topology of the constant-frequency surface is pointed out. The origin of the so-called phase transition of order two and a half is discussed.

Aim To study the condition of coronary vasculature by data of coronarography (CG) in patients with chronic ischemic heart disease (IHD) and arterial hypertension (AH) associated with stage 2-4 chronic kidney disease (CKD) and to evaluate the effect of a 12-week complex treatment with perindopril or with a combination of perindopril/amlodipine on changes in vascular wall stiffness, endothelial function, and structure and function parameters in this patient category after coronary stenting.Material and methodsr This study included 87 patients with chronic IHD and AH associated with stage 2-3 CKD for whom CG was performed due to ineffectiveness of the antianginal therapy. The patients were divided into three subgroups: subgroup 1 included 28 patients who received a conservative treatment with perindopril 10 mg/day; subgroup 2 consisted of 25 patients who underwent coronary stenting and were prescribed perindopril; subgroup 3 consisted of 34 patients who underwent stenting and were prescribed the perindopril/amlodipine combination. The reference group included 47 patients with IHD and AH with preserved kidney function. Anatomic and functional parameters of the heart, arterial stiffness, pulse wave velocity, cardio-ankle vascular index, augmentation index, central aortic systolic and pulse pressure, endothelium-dependent vasodilation, plasma concentration of endothelin-1 (ET-1), and plasma concentration of nitric oxide metabolites were evaluated at baseline and after 12 weeks of treatment.Results In patients with IHD, AH, and stage 2-3 CKD, arterial stiffness was more pronounced than in patients with preserved kidney function. Concentrations of ET-1 were significantly higher and levels of nitric oxide were lower in CKD. Supplementing the complex therapy with perindopril resulted in a considerable hypotensive effect in all subgroups, improvement of the kidney function, and positive dynamics of arterial stiffness and endothelial function. Changes in these parameters were more pronounced in patients after coronary stenting than in patients receiving only a conservative treatment. The use of perindopril/amlodipine following stenting exerted the most significant angioprotective and cardioprotective effect.Conclusion Patients with IHD and AH in combination with early CKD have pronounced impairment of the condition of arterial blood vessels and the heart. Addition of perindopril to the treatment not only exerted a hypotensive effect but also beneficially influenced mechanisms of progression of this combined pathology.

Interacting dark energy models may play a crucial role in explaining several important observational issues in modern cosmology and also may provide a solution to current cosmological tensions. Since the phenomenology of the dark sector could be extremely rich, one should not restrict the interacting models to have a coupling parameter which is constant in cosmic time, rather allow for its dynamical behaviour, as it is common practice in the literature when dealing with other dark energy properties, as the dark energy equation of state. We present here a compendium of the current cosmological constraints on a large variety of interacting models, investigating scenarios where the coupling parameter of the interaction function and the dark energy equation of state can be either constant or dynamical. For the most general schemes, in which both the coupling parameter of the interaction function and the dark energy equation of state are dynamical, we find 95% CL evidence for a dark energy component at early times and slightly milder evidence for a dynamical dark coupling for the most complete observational data set exploited here, which includes CMB, BAO and Supernova Ia measurements. Interestingly, there are some cases where a dark energy component different from the cosmological constant case at early times together with a coupling different from zero today, can alleviate both the H0 and S8 tension for the full dataset combination considered here. Due to the energy exchange among the dark sectors, the current values of the matter energy density and of the clustering parameter σ8 are shifted from their ΛCDM-like values. This fact makes future surveys, especially those focused on weak lensing measurements, unique tools to test the nature and the couplings of the dark energy sector.

In this paper we describe the model of glide dislocation interaction with obstacles based on the planar curve dynamics. The dislocations are represented as smooth curves evolving in a slip plane according to the mean curvature motion law, and are mathematically described by the parametric approach. We enhance the parametric model by employing so called tangential redistribution of curve points to increase the stability during numerical computation. We developed additional algorithms for topological changes (i.e. merging and splitting of dislocation curves) enabling a detailed modelling of dislocation interaction with obstacles. The evolving dislocations are approximated as a moving piece-wise linear curves. The obstacles are represented as idealized circular areas of a repulsive stress. Our model is numerically solved by means of semi-implicit flowing finite volume method. We present results of qualitative and quantitative computational studies where we demonstrate the topological changes and discuss the effect of tangential redistribution of curve points on computational results.

The topological properties of the charge distribution of 1,2‐dioxethane along the dissociation path (to formaldehyde products) and in different Hartree–Fock solutions are presented. At the equilibrium geometry of 1,2‐dioxethane, all bond paths do not coincide with the corresponding internuclear axes. The outward curvature of the OO bond path elaborates upon the concept of strain in the dioxethane ring. This weak binding of the ring is further confirmed by the considerably low ρ(r) value at the ring (3, +1) saddle point. An extension of the theory to the dynamic case has been discussed in terms of the topological changes in ρ(r) along the reaction path. The catastrophe of the chemical change, i.e., rupture of the dioxethane ring, takes the form of gradual merging and annhilation of the OO (3, −1) and the ring (3, +1) critical points. The values of ρ(r) at the positions of the critical points along the reaction path provide a topological characterization and definition of “partial valence.” The difference between the topological behavior of ρ(r), as obtained by different HF solutions, along the reaction path is analyzed and discussed.